Which of the following system has maximum number of unpaired electrons ?

Options

A. `d^(4)`(octahedral , low spin )
B. `d^(6)`(tetrahedral , high spin )
C. `d^(6)`(octahedral , low spin )
D. `d^(9)`(octahedral)

Answer

To determine which of the given systems has the maximum number of unpaired electrons, we will analyze each system step by step.

### Step 1: Analyze d4 in an Octahedral Low Spin Complex
- **Electron Configuration**: d4 means there are 4 electrons in the d-orbitals.
- **Orbital Splitting**: In an octahedral field, the d-orbitals split into two sets: 3 lower energy T2g orbitals and 2 higher energy Eg orbitals.
- **Filling Electrons**: For a low spin complex, electrons pair up in the lower energy T2g orbitals before occupying the higher energy Eg orbitals.
- T2g: 1, 2, 3 (3 electrons fill the T2g orbitals)
- Eg: 4 (the 4th electron pairs with one of the T2g electrons)
- **Unpaired Electrons**: There are 2 unpaired electrons.

### Step 2: Analyze d6 in a Tetrahedral High Spin Complex
- **Electron Configuration**: d6 means there are 6 electrons in the d-orbitals.
- **Orbital Splitting**: In a tetrahedral field, the d-orbitals split into two sets: 3 lower energy T2 orbitals and 2 higher energy E orbitals.
- **Filling Electrons**: For a high spin complex, electrons fill the orbitals singly before pairing occurs.
- T2: 1, 2, 3, 4, 5, 6 (all electrons occupy the T2 and E orbitals singly)
- **Unpaired Electrons**: There are 6 unpaired electrons.

### Step 3: Analyze d6 in an Octahedral Low Spin Complex
- **Electron Configuration**: d6 means there are 6 electrons in the d-orbitals.
- **Orbital Splitting**: In an octahedral field, the d-orbitals split into T2g and Eg.
- **Filling Electrons**: For a low spin complex, electrons pair up in the T2g orbitals before occupying the Eg orbitals.
- T2g: 1, 2, 3 (3 electrons fill the T2g orbitals)
- Eg: 4, 5, 6 (the remaining electrons pair up)
- **Unpaired Electrons**: There are 0 unpaired electrons.

### Step 4: Analyze d9 in an Octahedral Complex
- **Electron Configuration**: d9 means there are 9 electrons in the d-orbitals.
- **Orbital Splitting**: In an octahedral field, the d-orbitals split into T2g and Eg.
- **Filling Electrons**: The electrons fill the orbitals as follows:
- T2g: 1, 2, 3, 4, 5 (5 electrons fill the T2g orbitals)
- Eg: 6, 7, 8, 9 (the remaining electrons fill the Eg orbitals)
- **Unpaired Electrons**: There is 1 unpaired electron.

### Conclusion
After analyzing all four systems:
- d4 (octahedral low spin) has 2 unpaired electrons.
- d6 (tetrahedral high spin) has 6 unpaired electrons.
- d6 (octahedral low spin) has 0 unpaired electrons.
- d9 (octahedral) has 1 unpaired electron.

The system with the maximum number of unpaired electrons is the **d6 tetrahedral high spin complex**, which has **6 unpaired electrons**.

### Final Answer:
**The system with the maximum number of unpaired electrons is d6 tetrahedral high spin.**

---